M61-19

Question

5 couples sit on 10 chairs around a round table. If each couple must be seated together, how many possible arrangements are there?

A. 256
B. 512
C. 768
D. 1,024
E. 1,080

MathRevolution · Answer

Official Solution:

5 couples sit on 10 chairs around a round table. If each couple must be seated together, how many possible arrangements are there?

A. 256
B. 512
C. 768
D. 1,024
E. 1,080

The number of arrangements of the 5 couples in a circle is  (5-1)! = 4! . The members of each couple can be arranged in  2!  ways. Thus, the total number of arrangements is  4! * 2! * 2! * 2! * 2! * 2! = 24*2*2*2*2*2 = 768 .

Answer: C

Edyope · Answer

Is there a simpler way to solve this problem? It is not clear for me
Thank you

Voyagegrande · Answer

I think this is a  high-quality  question and the explanation isn't clear enough, please elaborate. can someone please explain the solution?

azizgmat · Answer

Since couples have to sit together you can think question as it asks for how many arrangements with 5 people is possible in a table at first. Since this is a round table (not a line) 5 people can sit chairs with 4! different arrangements. If it would be a line, number of arrangements would be 5! however, in a round table, every 4 of 5 different arrangements would be the same unlike a line (this is not very easy to understand). Shortly, 4! makes 24 and in the second step, since every element of our arrangements (I mean couples) has two members, they actually can change their places while sitting together. So, for every couple you should add (2) as multiplier to the number of arrangements which in total makes 4!x2^5.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

M61-19

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